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The average area of 3 square rooms I, II, and III are 1600 square meters. If one rectangular room(IV) area is added then the average area becomes 1400 square meters. If another room V, whose area is 400 square meters more than the IV room, replaces room I, then the average area of II, III, IV, and V room becomes 1350 square meters. Find the area of I room.

The average area of 3 square rooms I, II, and III are 1600 square meters. If one rectangular room(IV) area is added then the average area becomes 1400 square meters. If another room V, whose area is 400 square meters more than the IV room, replaces room I, then the average area of II, III, IV, and V room becomes 1350 square meters. Find the area of I room. Correct Answer 1400 square meters

Given:

The average area of I, II, and III room = 1600 square meters

The average area of I, II, III, and IV room = 1400 square meters

Area of Vroom = Area of IV room + 400 square meters

The average area of II, III, IV, and V room = 1350 square meters

Formula used:

Average = Sum of all the observation / Total number of observation

Calculation:

Area of (I + II + III) room = 4800      ….. (1)

Area of (I + II + III + IV) = 5600      …..(2)

Area of (II + III + IV + V) = 5400      ….(3)

From (1) and (2)

⇒ 4800 + IV = 5600

⇒ IV = 5600 – 4800

⇒ IV = 800

Area of V room = 800 + 400

= 1200 square metres

From (3)

⇒ II + III + 800 + 1200 = 5400

⇒ II + III = 5400 – 2000

⇒ II + III = 3400       ….. (4)

From (1) and (4)

⇒ I + 3400 = 4800

⇒ I = 4800 – 3400

⇒ I = 1400

∴ The area of I room is 1400 square meters.

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